Distribution of CEO Ages The distribution of ages of CEOs is...

Distribution of CEO Ages The distribution of ages of CEOs is as follows: $$ \begin{array}{ll}{\text { Age }} & {\text { Frequency }} \\ \hline 21-30 &\quad\quad { 1 } \\ {31-40} &\quad\quad {8} \\ {41-50} &\quad \quad{27} \\ {51-60} & \quad\quad{29} \\ {61-70} &\quad\quad {24} \\ {71-4 p} & \quad\quad{11}\end{array} $$ If a CEO is selected at random, find the probability that his or her age is a. Between 31 and 40 b. Under 31 c. Over 30 and under 51 d. Under 31 or over 60

Distribution of CEO Ages The distribution of ages of CEOs is as follows:
$$
\begin{array}{ll}{\text { Age }} & {\text { Frequency }} \\ \hline 21-30 &\quad\quad { 1 } \\ {31-40} &\quad\quad {8} \\ {41-50} &\quad \quad{27} \\ {51-60} & \quad\quad{29} \\ {61-70} &\quad\quad {24} \\ {71-4 p} & \quad\quad{11}\end{array}
$$
If a CEO is selected at random, find the probability that his or her age is
a. Between 31 and 40
b. Under 31
c. Over 30 and under 51
d. Under 31 or over 60

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Key Concepts

Relative Frequency

Relative frequency is the ratio of the frequency of a specific outcome to the total number of outcomes. It provides an estimate of the probability of that outcome and is particularly useful in situations where probabilities are derived from observed data, such as the age intervals for CEOs.

Event Operations in Probability

Event operations, including union and intersection, are used to combine or separate multiple outcomes when calculating probabilities. For instance, selecting a CEO 'under 31 or over 60' involves the union of two mutually exclusive age groups, and understanding how to combine these probabilities is a key concept in the analysis.

Probability

Probability is the measure of the likelihood that an event will occur, calculated by dividing the number of favorable outcomes by the total number of outcomes in the sample space. In this context, it is used to determine the chance that a randomly selected CEO falls within a specified age range based on the frequency distribution.

Frequency Distribution

A frequency distribution is a tabular representation that shows the number of occurrences of each value or range of values in a data set. In this problem, the ages of CEOs are grouped into intervals with corresponding frequencies, which provide the basis for calculating probabilities for different age ranges.

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